Represent Rational Numbers in Number Line (Part - 8) - Rational Numbers , Maths, Class 7 Video Lecture

hello friends this video on rational
numbers part eight is brought to you by
exam feel calm no more fear from exam so
now that we got a basic idea about what
are rational numbers now it is time to
see where are they located on the
numbers and so by now all of you know
what is a number line so as you can see
on the screen it is the line where we
locate different numbers so till now we
saw the natural numbers whole numbers
integers on a number line
now quite interesting to know where
exactly do we see rational numbers
because when you look at the number line
we can see the natural numbers one two
three four we can see the whole numbers
from zero we can also see the integers
both positive and negative on the number
line but do you see the rational numbers
on the number line for example do you
see three by two on the number line I
did not see it as such but this also
exists on the number line so here we
will see how or and where do we
represent Mac rational numbers on a
number line so what we will do now is we
will try to represent some very very
simple rational numbers so let us take
the example of one of the most simplest
rational number one by two
what does one buy do now it lit in
literal terms if I ask you what is 1 by
2 you would say 1 by 2 is half now any
approximate idea where 1/2 should line
so 1/2 means it is less than 1 right so
if I tell you I will give you half a
chocolate that means am I going to give
you 1 chocolate no I am going to give
you less than 1 chocolate correct so but
at the same time 1/2 is greater than 0
so 1/2 lies somewhere between 0 and 1
somewhere between these two lies 1/2 so
how do we represent exact position of 1
by 2 so what we do is once we have an
approximate idea that okay lies between
0 & 1 we divide this region into two
equal parts
I do equal parts because one by two is
one part of two parts so basically we
need to divide this region into two
equal parts so this is one part this is
another part right now what is 1 by 2 1
by 2 basically means one part out of two
parts so one part is with this much part
out of two parts so basically one by two
would mean this point because this point
signifies one part out of two parts so
this is where one by two lines so one by
two lines exactly midway between zero
and one let us look at one more example
it is take the next example of 1 by 3 so
1 by 3 is also a rational number so
where do you think 1 by 3 would lie 1 by
3 is 1/3 of something so this is also
less than 1 but greater than 0 so this
also lies somewhere between 0 and 1 now
how do we know where exactly lies how
what will we do it is one part out of
three parts so the denominator is 3
therefore we will divide this region
into three equal parts one part two part
and three part so that this is how we
have divided it into three equal parts
and this one by three is one part out of
three parts so this is one part out of
three parts or this would be 1 by 3 so
this point is 1 by 3 so you see this
point is 1 by 3 which point would be 2
by 3 so this point the next point would
be 2 by 3 so this this point would be 2
by 3 so what would be this point this
point would be 3 by 3 so 3 by 3 is
nothing but 1 that is what it is this
one next so you see in this fashion we
can actually determine the exact
position of a rational number let's take
one more example let's talk about 1 by 4
so 1 by 4 again lies between 0 & 1 how
do we know it here we will divide it
into four equal parts
so you see 1 2 3 & 4 so these are 4
equal parts of one part out of 4 parts
so this is 1 by
so this is the exact location of one by
four so this is the pattern by which we
can actually precisely tell the location
or very exactly a rational number like
on a number line at least with these
examples you've got to know that okay
even though we do not directly see the
rational numbers on the number line but
still they are also there so let us try
to locate five by four on a number line
five by four is again a rational number
so in order to even as I said that you
should have an approximate idea about
where this rational number ties between
which two whole numbers at least it is
that much idea should be there so what
do you do is you convert this five by
four into mixed fractions right now it
is improper fraction right so it is
converted into mixed fraction so five by
four so if you divide it you get four
ones of four one so basically if you
convert it into mixed fraction 5 by 4 is
equal to 1 1 by 4 that means this number
is greater than the whole number 1 so it
is greater than one but it is less than
2 so with this we see that it lies
between 1 & 2 so let us draw the number
line so we have magnified the number
line so that we can see this region
between 1 & 2 more closely so this is 1
and this is 2 now we have to locate 5 by
4 so what are we going to do okay so now
we are going to divide this particular
region that means one unit from so from
0 to 1 we are going to divide it into
four equal parts that is what we have
done right five parts out of four parts
so denominator this 4 so we will divide
this region into four equal parts 1 2 so
this is 1 2 3 4 similarity 1 2 2 3 & 4
so here also 1 2 3 4 so this is how we
have divided each section that is
each unit the distance between two whole
numbers into four equal parts now you
see this so what would be this part this
part would be one part out of four parts
so this would be 1 by 4 this would be 2
by 4 this would be 3 by 4 this would be
4 by 4 this would be 5 by 4 so basically
this is the point that we've been
looking for so in this way we can locate
5 by 4 so every time what you need to do
is first get a rough idea about where
this number is located at least between
which two whole numbers
so once you got an idea then what you do
is you divide each part that is each
part would mean each segment between two
whole numbers into those many equal
parts which is the denominator so in
this case the denominator is 4 therefore
we have divided each section into four
equal parts so this is the strategy that
you need to follow to locate a rational
number on a number line now when you
look at this process you will find that
it is very similar to how we locate
fractions on a number line so we have
already learned how to locate fractions
on a number line this is a this is the
same that typically is the typical
procedure that we follow to locate
fractions on a number line let's locate
minus 3 by 2 on a number line so minus 3
by 2 would be towards the left hand side
of 0 it's because positive rational
numbers is towards the right so the
positive rational numbers is towards the
right and the negative rational numbers
as towards the length so let us first
get an idea about where minus 3 by 2
would be located between which two whole
numbers so for that let us first convert
3 by 2 into mixed fractions so what do
you get so you see that minus 3 by 2 is
nothing but minus 1 1 by 2 so looking at
this you can see that it is greater than
1 but it is less than 2 therefore where
does it lie it lies between minus 1 and
because it is negative right so it lies
somewhere between these two now where
exactly between these two so for that we
have to divide this each section into
two equal parts because the denominator
is 2 so divide it into two equal parts
divide this into two equal parts
so what would be this point this point
is one part out of two parts so this is
minus 1 by 2 what is this this is minus
2 by 2 this is minus 3 by 2 this is
minus 4 Bible so what is we have wanted
to locate at this point minus 3 by 2 so
this is where this would be located you
see you follow the same simple steps and
every day we would be able to locate the
rational number of number line thank you
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